1. Field of the Invention
The present invention relates to impulse noise estimation and removal in orthogonal frequency division multiplexing (OFDM) transmissions, and particularly to transmissions in power line communications and digital subscriber line (DSL) transmissions.
2. Description of the Related Art
Signal transmissions, such as those delivered via power line communications and digital subscriber line (DSL) transmission, must cope with intersymbol interference (ISI) distortion, additive white Gaussian noise (AWGN) and impulse noise. In telecommunication, intersymbol interference is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon, as the previous symbols have similar effect as noise, thus making the communication less reliable. ISI is often caused by multipath propagation and the inherent non-linear frequency response of a channel. ISI arises due to imperfections in the overall frequency response of the system. The presence of ISI in the system, however, introduces errors in the decision device at the receiver output. Therefore, in the design of the transmitting and receiving filters, the objective is to minimize the effects of ISI, and thereby deliver the digital data to its destination with the smallest error rate possible. Common techniques to fight against intersymbol interference include adaptive equalization and error correcting codes.
In communications, the additive white Gaussian noise channel model is one in which the information is given a single impairment, i.e., a linear addition of wideband or white noise with a constant spectral density (typically expressed as Watts per Hertz of bandwidth) and a Gaussian distribution of noise samples. The model does not account for the phenomena of fading, frequency selectivity, interference, nonlinearity or dispersion. However, it produces simple and tractable mathematical models that are useful for gaining insight into the underlying behavior of a system before these other phenomena are considered.
Wideband Gaussian noise comes from many natural sources, such as the thermal vibrations of atoms in antennas (referred to as thermal noise or Johnson-Nyquist noise), shot noise, black body radiation from the Earth and other warm objects, and from celestial sources such as the Sun. As an example of noise in signal transmissions, ADSL/VDSL over short distances operates at an extremely high signal-to-noise ratio (SNR) with very high spectral efficiencies (quadrature amplitude modulation, or “QAM”, constellations of up to 215 points can be used), and their main limiting factor is impulse noise and cross-talk, rather than AWGN. As will be described in greater detail below, impulse noise estimation and cancellation at the receiver is of particular interest and importance.
Impulsive noise is considered one of the biggest challenges in DSL technology and OFDM transmission in general. While impulsive noise is often attributed to switching electronic equipment, there is no general consensus as to the proper modeling of impulsive noise. There are various ways to deal with errors that take place at the physical layer in DSL. Forward error correction is one common way of counteracting, or accounting for, such errors. Specifically, a superframe in DSL implements an inner convolutional code with an interleaver and a Reed-Solomon outer code. The interleaver spreads the impulse noise errors around the signal, allowing the code redundancy to better deal with these errors.
Alternatively, other common techniques attempt to detect the presence of impulses and their locations, and use this information to enhance the performance of forward error correction (FEC). One common method detects the presence of an impulse using a thresholding scheme, and then erases the whole OFDM block in order not to exceed the error correction capability of the channel coding. Most standardized approaches try to detect or forecast the location of the errors. With this knowledge, one can theoretically detect twice as many errors as when the location of the errors is unknown. When the physical layer is not able to deal with erasures through forecasting and FEC, the physical layer tags the uncertain discrete multitone (DMT) symbols and sends them to higher layers.
Pre-coding techniques and frequency algebraic interpolation techniques inspired by Reed-Solomon coding and decoding over the complex numbers have been proposed to cope with this problem. Specifically, the presence of impulse noise within a few samples creates certain syndromes in a sequence of pilots or null frequencies, which can be used to detect the location of impulse noise, estimate it, and cancel the noise. The problems with such techniques are that they require a certain structure of the null frequencies or pilots, they are guaranteed to detect only a limited number of impulse noise samples, and they can be very sensitive to background noise (to the extent that some intermediate step is needed to ensure that the algorithm does not malfunction).
In FIG. 3, the relevant time-domain complex baseband equivalent channel is given by:
                              y          k                =                                            ∑                              l                =                0                            L                        ⁢                                                  ⁢                                          h                l                            ⁢                              x                                  k                  -                  l                                                              +                      z            k                    +                      e            k                                              (        1        )            where xk and yk denote the channel input and output, h=(h0, . . . hL) is the impulse response of the channel, zk represents AWGN and is independent and identically distributed (i.i.d.) drawn from a zero mean normal distribution with variance N0 (the noise), or ˜(0, N0), and ek is an impulsive noise process, which, for purposes of this analysis, is assumed to be Bernoulli-Gaussian, i.e., ek=λkgk, where λk are i.i.d. Bernoulli random variables, with P(λk=1)=p, and gk are i.i.d. Gaussian random variables ˜CN(0, I0). The channel SNR is defined as Ex/N0, and the impulse to noise ratio (INR) is defined as I0/N0.
FIG. 3 illustrates a typical, simplified OFDM prior art system 100, including transmitter T, receiver R and an intermediate channel C. Here, the channel model of equation (1) takes the matrix form:y=Hx+e+z  (2)where y and x are the time-domain OFDM receive and transmit signal blocks (after CP removal) and z˜CN(0,N0I). The vector e is an impulse noise process and, specifically, e is a random vector with support e) (a set of the non-zero components) uniformly distributed over all
      (                            m                                      s                      )     possible supports of cardinality s<<m, and i.i.d. non-zero components ˜CN(0, I0).
Due to the presence of the cyclic prefix, H is a circulant matrix describing the cyclic convolution of the channel impulse response with the block x. Letting F denote a unitary discrete Fourier transform (DFT) matrix with (k, l) elements
                    [        F        ]                    k        ,        l              =                  1                  n                    ⁢              ⅇ                              -            j                    ⁢                                          ⁢          2          ⁢          π          ⁢                                          ⁢                      kl            /            n                                ,with k,lε{0, . . . , n−1}, the time domain signal is related to the frequency domain signal by:
                    x        =                              1                          n                                ⁢                      F            H                    ⁢                      x            ⋁                                              (        3        )            and, furthermore, given a circulant convolution matrix H,H=FHDF  (4)where D=diag({hacek over (h)}) and {hacek over (h)}=√{square root over (nFH)} is the DFT of the channel impulse response (whose coefficients are found, by construction, on the first column of H).
Demodulation amounts to computing the DFT, as given in equation set (5) below:
                                                                        y                ⋁                            =              Fy                                                                          =                                                diag                  ⁢                                                                          ⁢                                      (                                                                  H                        0                                            ,                      …                      ⁢                                                                                          ,                                              H                                                  m                          -                          1                                                                                      )                                    ⁢                                      x                    ⋁                                                  +                                                      F                    H                                    ⁢                  z                                +                                                      F                    H                                    ⁢                  e                                                                                                        =                                                D                  ⁢                                      x                    ⋁                                                  +                                  z                  ⋁                                +                Fe                                                                        (        5        )            where
      H    i    =            ∑              k        =        0            L        ⁢                  ⁢                  h        l            ⁢              ⅇ                  j          ⁢                                    2              ⁢              π                        n                    ⁢          li                    are the DFT coefficients of the channel impulse response, and {hacek over (z)}=Fz has the same distribution of z. Without impulsive noise, it is well known that equation set (5) reduces to a set of m parallel Gaussian channels: {hacek over (y)}i=Hi{hacek over (x)}i+{hacek over (z)}i, for i=1, . . . , m.
In the presence of the impulsive noise, the performance of a standard OFDM demodulator may dramatically degrade since even a single impulse in an OFDM block may cause significant degradation to the whole block. This is because {hacek over (e)}=Fe can have a large variance per component, and, thus, affects more or less evenly all symbols of the block.
Thus, a method of estimating and removing noise in OFDM systems solving the aforementioned problems is desired.